Post-fault dynamics of short-term voltage stability (SVS) present spatial-temporal characteristics, but the existing data-driven methods for online SVS assessment fail to incorporate such characteristics into their models effectively. Confronted with this dilemma, this paper develops a novel spatial-temporal graph convolutional network (STGCN) to address this problem. The proposed STGCN utilizes graph convolution to integrate network topology information into the learning model to exploit spatial information. Then, it adopts one-dimensional convolution to exploit temporal information. In this way, it models the spatial-temporal characteristics of SVS with complete convolutional structures. After that, a node layer and a system layer are strategically designed in the STGCN for SVS assessment. The proposed STGCN incorporates the characteristics of SVS into the data-driven classification model. It can result in higher assessment accuracy, better robustness and adaptability than conventional methods. Besides, parameters in the system layer can provide valuable information about the influences of individual buses on SVS. Test results on the real-world Guangdong Power Grid in South China verify the effectiveness of the proposed network.